Photonic chips based on multimode fiber-to-waveguide coupling

ABSTRACT

Optical coupling designs are disclosed to provide a photonic device, for example, that includes a substrate; an optical waveguide formed on the substrate and configured as a multimode waveguide to support light in different optical waveguide modes; and an optical fiber structured as a multimode fiber to support light in different optical fiber modes, the optical fiber located above the optical waveguide and optically coupled to the optical waveguide via evanescent coupling to allow light to be coupled between the optical fiber and the optical waveguide.

PRIORITY AND RELATED APPLICATION

This patent document timely claims the priority of U.S. ProvisionalApplication No. 62/159,117 entitled “PHOTONIC CHIPS BASED ON MULTIMODEFIBER-TO-WAVEGUIDE COUPLING” and filed May 8, 2015, which isincorporated by reference as part of this patent document.

TECHNICAL FIELD

This patent document relates to optical coupling between a fiber and awaveguide and its applications in photonic chips and other devices orapplications.

BACKGROUND

In various applications, there is a need to couple light between a fiberand an optical waveguide. Due to the differences in structure betweenfiber and optical waveguides and due to optical alignment between thefiber and optical waveguide, such coupling tends to exhibit some opticalloss and may vary depending on the alignment between the fiber andwaveguide.

SUMMARY

The disclosed technology can be implemented to couple the optical modesfrom a multimode fiber to the modes of an integrated waveguide. In oneembodiment, each fiber mode corresponds to a defined waveguide mode.This allows for selective handling of the spatial modes of the fiber inthe fiber-waveguide coupling. Routing or filtering, for example, may bedone on certain modes individually. In some embodiments, the integratedmultimode coupler formed by the multimode fiber and the waveguide iscoupled to a mode demultiplexer and feeds coupled light into the modedemultiplexer. After this demultiplexer, the light processing may bedone using integrated single mode waveguides.

In one aspect, a photonic device is provided to include a substrate; anoptical waveguide formed on the substrate and configured as a multimodewaveguide to support light in different optical waveguide modes; and anoptical fiber structured as a multimode fiber to support light indifferent optical fiber modes, the optical fiber located above theoptical waveguide and optically coupled to the optical waveguide viaevanescent coupling to allow light to be coupled between the opticalfiber and the optical waveguide.

In another aspect, a photonic device is provided to include a substrate;and an input/output multimode optical waveguide formed on the substrateand configured to support light in different optical waveguide modes asan input/output optical port of the substrate. The input/outputmultimode optical waveguide includes a tapered waveguide terminal thatdecreases in cross section towards a tip of the tapered waveguideterminal. This device further includes an optical multimodemultiplexing/demultiplxing coupler coupled to the input/output multimodeoptical waveguide to either receive different optical signals indifferent optical single modes to combine the received different opticalsignals into a multimode signal to the input/output multimode opticalwave, or to receive a multimode optical signal from the input/outputmultimode optical wave to split the received multimode optical signalinto different optical signals in different optical single modes; and aplurality of single mode optical waveguides formed on the substrate andoptically coupled to the input/output multimode optical waveguide toguide, respectively, the different optical signals in different opticalmodes, either from the input/output multimode optical waveguide or tothe input/output multimode optical waveguide. In addition, opticalprocessing modules are formed on the substrate and coupled to the singlemode optical waveguides, respectively, and each optical processingmodule is configured to process a respective optical signal of a singleoptical mode. A multimode optical fiber is structured to support lightin different optical fiber modes and is located above the input/outputmultimode optical waveguide to be optically coupled to the input/outputmultimode optical waveguide via evanescent coupling to allow light to becoupled between the optical fiber and the input/output multimode opticalwaveguide. In this device, the multimode optical fiber includes atapered fiber terminal which decreases in cross section towards a tip ofthe tapered fiber terminal and thus tapers in an opposite direction fromtapering of the tapered waveguide terminal, and the tapered fiberterminal and the tapered waveguide terminal spatially overlap with eachother to cause adiabatic transition of guided light and to causecoupling of different modes between the tapered fiber terminal and thetapered waveguide terminal.

In yet another aspect, a method is provided for using a multimodeoptical coupler in coupling light and includes spatially overlapping afirst multimode optical waveguide having a first spatially taperedwaveguide terminal to adiabatically transition light in different firstoptical modes with a second multimode optical waveguide having a secondspatially tapered waveguide terminal to adiabatically transition lightin different first optical modes in an opposite tapering direction of atapering direction of the first spatially tapered waveguide terminal,causing optical coupling between the first optical modes and the secondoptical modes; and using the first multimode optical waveguide to guidemultimode light in the first optical modes into the second multimodeoptical waveguide in the second optical modes.

Those and other features of the disclosed technology area described ingreater detail in the drawings, the description and the claims.

BRIEF DESCRIPTION OF DRAWINGS

FIGS. 1A, 1B and 1C show an example of a Fiber-to-Chip Multimode Couplerthat implements the disclosed technology. FIG. 1A shows the fiber taper(or a polymer waveguide taper) and the on-chip waveguide taper. FIG. 1Band FIG. 1C show two different cross-section views of the coupler inFIG. 1A.

FIG. 2 shows an example of results of power coupling simulation from thecoupler shown in FIGS. 1A, 1B and 1C formed by a six-mode multimodefiber and a SiN multimode waveguide. This shows an average of 50%coupling from all the fiber modes.

FIG. 3 shows an example of Fiber-to-Chip Multimode Signal Processing.The upper image shows the first stage of an on-chip multimode processor.The fiber-to-chip multimode coupler will convert the fiber modes to themodes within a waveguide. The mode-demultiplexer will convert the modesof the waveguide to single mode waveguides for processing.

FIG. 4 shows different coupler arrangements and geometries.

DETAILED DESCRIPTION

An optical waveguide formed on a substrate can be used to receive lightfrom a source off the substrate and to provide the received light to aphotonic circuit formed on the substrate or to export the light from thephotonic chip out of the chip. A fiber can be optically coupled to thewaveguide to deliver the light into the waveguide or to receive thelight from the waveguide. When the fiber is a multimode fiber and thewaveguide is a multimode waveguide, there can be a significant or largemode-mismatch between the multimode fiber and the on-chip waveguide. Amode can be an optical mode supported by a fiber or waveguide, includingdifferent polarization spatial modes. A mode mismatch can lead to poorcoupling efficiency between the fiber and the waveguide and loss of muchof the information and power held in the fiber's modes. Efficientoptical coupling from the multiple spatial modes of a multimode fiber towaveguides on-chip for individual signal processing is more difficultsingle mode coupling between a single-mode waveguide and a single-modefiber. Tiecke et al. demonstrated using a tapered single mode fiber andsingle mode waveguide for efficient fiber-to-chip coupling throughadiabatic evanescent coupling (about 97%) in an article entitled“Efficient fiber-optical interface for nanophotonic devices” in Optica2015; 2: 70-75 (2015).

The technology disclosed in this patent document can be used to providea conversion for multimode fiber to on-chip waveguides, which, even at arelatively low efficiency, would be very useful for telecommunicationsand signal processing. Spatial mode multiplexing is a promising newtechnology for high data rate transmission. The coupling between themultimode fiber and the on-chip waveguide based on the disclosedtechnology in this patent document uses a side by side placement of themultimode fiber and the multimode waveguide via evanescent couplingbetween them. Some aspects of such side by side placement of a waveguideon a chip and a fiber off the chip are disclosed in the CornellUniversity's U.S. Patent Publication No. US20160077282A1 entitled“Fiber-waveguide evanescent coupler” by inventors Michal Lipson andBiswajeet Guha, which was included as part of the U.S. ProvisionalApplication No. 62/159,117 and is incorporated by reference as part ofthis patent document.

Implementations of the disclosed technology can use an adiabatic couplerto convert the modes of a multimode fiber as one system to the modes ofa waveguide on an integrated photonic chip as another system. Thetransition between two multimode systems can be configured to beoptically adiabatic to achieve nearly lossless or efficient one-to-onemode coupling between the two systems. This adiabatic condition can beachieved by structuring the optical waveguide to include a taperedwaveguide terminal, structuring the optical fiber to include a taperedfiber terminal, and placing the tapered fiber terminal of the fiber overthe tapered waveguide terminal on the substrate to spatially overlapwith the tapered waveguide terminal of the optical waveguide. Thisstructure provides a multimode fiber-to-chip mode coupler.

FIGS. 1A, 1B and 1C illustrate an example of such a multimodefiber-to-chip mode coupler. As illustrated, the multimode fiber has afiber terminal that is positioned over the chip substrate to align withthe waveguide terminal of a multimode optical waveguide formed on thesubstrate of the photonics chip as illustrated by the top view in FIG.1A. The waveguide terminal is an input/output (I/O) port of the chip toreceive light from the fiber or to export light from the chip to thefiber. FIG. 1B shows a first side view of a cross section of the coupleralong line B-B′ that is perpendicular to the fiber and the waveguidewhere the fiber terminal is shown to be vertically displaced above thewaveguide terminal on the substrate. In this illustrated example, thefiber core of the multimode fiber is lager in cross section than that ofthe waveguide terminal. FIG. 1C shows a second view of a cross sectionof the coupler along line C-C′ that is parallel to and is along thecenter of the fiber and the waveguide where the fiber cladding in thetapered fiber terminal is removed.

In operation, the fiber-to-chip mode coupler having the spatiallyoverlap between the tapered multimode fiber and the tapered on-chipwaveguide to cause an evanescent coupling vertically. Both the multimodefiber and multimode waveguide may be tapered to delocalize theirrespective optical modes. The tapering in the fiber terminal causes theoptical modes of the fiber to slowly transition to the modes of thewaveguide. In the illustrated example in FIG. 1A, the fiber is tapereduniformly (or radially) by pulling the fiber with controlled automatedstages as heat is applied, shrinking its diameter, but not too thin soas to no longer support all of the higher-order modes. The fiberdiameter may be, for example, greater than 200 nm and less than 200 or300 micrometers (e.g., less than 20 micrometers in someimplementations). The integrated waveguide is fabricated using standardlithography and etching techniques.

In some implementations, the waveguide material may be a CMOS compatiblematerial such as silicon or silicon nitride, and may be structured tohave an index of refraction greater than 1.3 and less than 5. Thewaveguide may be clad with another material of a lower index asindicated by the “upper waveguide cladding” in FIG. 1C and may also beclad air without the upper cladding. The separation between theintegrated waveguide and the fiber may range from direct contact to somespacing, e.g., several micrometers in some applications, based on thedesired evanescent coupling needed between the fiber terminal and thewaveguide terminal. For stronger interaction of the evanescent field tothe fiber, the waveguide can be left unclad.

The tapering length of the fiber and tapering length of the waveguidecan be selected and optimized for the desired coupling and may bedetermined by, for example, simulating power transfer between the fiberand the waveguide. Simulations in FIG. 2 show that at least 50% of thepower in a 6-mode fiber can be coupled to a multimode waveguide. Thesimulation is for a specific geometry of waveguide and fiber which canbe optimized for better coupling.

In implementing the disclosed technology, the tapered fiber can bebrought close to the waveguide taper to vertically couple the inputlight from the fiber. This vertical distance as shown in FIG. 1B and 1Ccan be optimized given the geometry of the fiber and the waveguide andmaterials used in the fiber and the waveguide. Conducted simulationssuggest efficient coupling can be achieved by direct contact between thetapered fiber terminal and the tapered waveguide (zero or near zerovertical spacing) or by some small spacing up a certain verticaldistance limit based on the needed coupling efficiency (e.g., 1micrometer but usually less than 500 nm in some examples). In practicaldevice implementations, this vertical spacing can be achieved usingvarious mechanisms, including, e.g., micro-positioning stages or otheractuated support for providing an adjustable control over the verticalspacing, or packaging of the fiber to the chip which can also be used tohold the fiber in place permanently. The coupling may also be aided byusing a fluid between and surrounding the waveguide and fiber toengineer the index contrast and thus mode size and shape.

FIG. 3 shows an example of on-chip multimode processing based on thefiber-waveguide coupler in FIGS. 1A-1C as an input or output port of aphotonics chip. The multimode waveguide is coupled by a demultiplexer todifferent single mode waveguides and the multimode light isdemultiplexed to different optical signals in single modes that are fedinto different single mode waveguides, respectively. This can beaccomplished by using various demultiplexing techniques, e.g., usingasymmetric directional couplers or ring resonators. The single modewaveguides can be used for signal processing including filtering andmodulation. After the single-mode processing in the single-modewaveguides, the signals may be coupled back into a multimode waveguideby using a mode multiplexer on the chip and the light in the multimodewaveguide can be coupled to a multimode fiber using a fiber-to-chipmultimode coupler shown in FIGS. 1A-1C that is operated in a reverseprocess.

In implementations, various features may be used. For example, the fibermay be narrowed to a thinner diameter but not noticeably changingthroughout the coupling region; or it may be tapering during thecoupling. The fiber may be any type of waveguide with an index ofrefraction greater than that of its cladding, but less than that of thebottom waveguide as it tapers wider. The fiber may be a waveguide drawninto a long cylinder made of silica, for example. It alternately may bea polymer or dielectric of possibly rectangular shape which may bedefined lithographically over the waveguide. If the fiber waveguide is adeposited material such as a polymer, it may enclose the bottomintegrated waveguide or be vertically or horizontally separated or incontact. The waveguide may be single-mode or multimode at differentparts of the taper. The waveguide may be tapering or of constant widthat different parts during coupling. The beginning of the waveguide maybe a small point or width near the lithography limit, typically from10-100 nm.

In some applications, the disclosed technology can be used toefficiently collect power from all the modes of a fiber. This is usefulfor collecting the entire signal from a multimode fiber for use on-chip.Also, if the identity of the modes is captured by the correspondence offiber modes with waveguide modes, it is useful for on-chip signalprocessing. This could be used to increase data transmission rates inoptical communication by increasing the number of spatial mode channelsof fiber. The device could also be used in reverse to generate modes ofa fiber from on chip, or to return to a multimode fiber after arrivingon the chip after beginning with a different multimode fiber. Inreverse, the multimode waveguide may taper narrower as the modesadiabatically transfer into the fiber.

In various applications, various features may be used. For example, thefiber suitable for the disclosed coupler may be another multimodewaveguide such as a multimode polymer waveguide or another waveguidehaving an effective index of refraction of the mode larger than that ofthe integrated waveguide. Examples of the fiber include a silica fiber,a polymer waveguide, a dielectric waveguide formed of a material such assilicon oxynitride. When using a polymer waveguide off the chip forcoupling with the on-chip waveguide, the polymer waveguide may be shapedas a square or rectangular polymer material such as epoxy, acrylate,siloxane, or SU-8). FIG. 4 shows three examples of coupler arrangementsand geometries. The polymer index of refraction, index contrast, andsize can be designed to be nearly identical to that of a traditionalfiber in some implementations. The polymer index may be similar, lessthan, or greater than that of glass fiber, probably in the range 1.3 to2 (or 1.3 to 5 to be more inclusive). The polymer is not necessarily aCMOS compatible material. The light can be coupled from a multimodepolymer waveguide to the integrated e.g. silicon or silicon nitridewaveguide (“the waveguide”) in a nearly identical way. The polymerwaveguide could be integrated above the on-chip waveguide, placed on theside of the on-chip waveguide or even enclose the on-chip waveguide. Amultimode fiber can butt couple to the polymer waveguide with verylittle loss if the size and index contrast are similar or the modesmatch. The fiber could be placed in a groove or otherwise aligned to thepolymer waveguide. All of the modes go from the multimode fiber to themultimode polymer. Then the polymer waveguide's modes evanescentlycouple into the waveguide as the waveguide adiabatically tapers wider.The waveguide can be tapered with a sufficient taper width to supportthe number of modes desired to be taken from the multimode fiber orpolymer.

The disclosed multimode coupler with the tapers can be used for couplinghigher order modes from 2 or more modes to 3 or 4 or more modes invarious applications.

The disclosed multimode coupler can be implemented for variousapplications, including coupling light from multimode sources, such asVCSELs, which are typically coupled to multimode fibers, to a photonicintegrated chip; coupling with regard to mode content so that theoriginal distribution of power in the various modes of the fiber can bedetermined on the chip; coupling without regard to mode content suchthat it is simply desired to get the largest amount of power from thefiber onto the chip; coupling with intent to send back to multimodefiber (by using the adiabatic coupler in reverse, from multimodewaveguide adiabatically tapering narrower to couple to the fiber output,wherein while on chip some processing may or may not be done, and thisprocessing may possibly be done after demultiplexing to single modewaveguides.

In implementations, the effective index of the mode in the taperingwaveguide can be set to be equal to or greater than the mode in thefiber when they begin to couple. When the fiber and waveguide are close,and the waveguide has tapered sufficiently wide, a supermode exists andbegins to transition from being mostly confined in the fiber to beingmostly confined in the waveguide as the waveguide adiabatically taperswider. The fiber modes must have greater effective indexes than theindex of the waveguide cladding, if it is present, or else the waveguidemust taper wide enough to have an index at or above that of the fibermodes within a short distance from the beginning of the structure orelse the mode will leak into the cladding/substrate and be lost.

In some implementations, the shape of the waveguide tapering structuremay a linear taper as shown in FIG. 1A and may be in other non-lineartapering profiles, including, e.g., a parabolic taper profile. Thetapering may also be segmented into multiple segments of discrete orcontinuously varying taper angle, in order to optimize the size of theoverall structure or to design the mode mapping from the fiber to thewaveguide.

The disclosed technology can be used for light coupling of variouswavelengths, including, e.g., The wavelengths from 400 nm to 1.7 um andother wavelengths.

Different from what is shown in the example in FIG. 1A, the waveguide,once it adiabatically tapers, may be a width greater than or less thanthat of the fiber. The tapered waveguide terminal can be used to supportat least the number of modes as contained in the fiber, or at least asmany as are desired to be coupled. The initial width of the taper mayeither be a point or a fixed small width, such as the lithography limit(e.g. 100 nm). The sudden introduction of the endpoint may incur a smallloss and reflection. Rather than tapering the width of the waveguide,the device still works if the waveguide is multimode in the verticaldirection and vertically tapering wider, but this geometry is lesscommon to fabricate.

While this patent document contains many specifics, these should not beconstrued as limitations on the scope of any invention or of what may beclaimed, but rather as descriptions of features that may be specific toparticular embodiments of particular inventions. Certain features thatare described in this patent document in the context of separateembodiments can also be implemented in combination in a singleembodiment. Conversely, various features that are described in thecontext of a single embodiment can also be implemented in multipleembodiments separately or in any suitable subcombination. Moreover,although features may be described above as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination can in some cases be excised from thecombination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the Figures in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. Moreover, the separation of various system components in theembodiments described above should not be understood as requiring suchseparation in all embodiments.

Only a few implementations and examples are described and otherimplementations, enhancements and variations can be made based on whatis described and illustrated in this patent document and its Attachment.

What is claimed is:
 1. A photonic device, comprising: a substrate; anoptical waveguide formed on the substrate and configured as a multimodewaveguide to support light in different optical waveguide modes; and anoptical fiber structured as a multimode fiber to support light indifferent optical fiber modes, the optical fiber located above theoptical waveguide and optically coupled to the optical waveguide viaevanescent coupling to allow light to be coupled between the opticalfiber and the optical waveguide.
 2. The device as in claim 1, whereinthe optical waveguide includes a tapered waveguide terminal, the opticalfiber includes a tapered fiber terminal which spatially overlaps withthe tapered waveguide terminal of the optical waveguide.
 3. The deviceas in claim 2, wherein the tapered fiber terminal which spatiallyoverlaps with the tapered waveguide terminal of the optical waveguidehas a cross section that decreases towards a direction along which thetapered waveguide terminal of the optical waveguide has a cross sectionthat increases.
 4. The device as in claim 3, further comprising: one ormore photonic components or devices formed on the substrate to receivelight from or to send light to the optical fiber via the opticalwaveguide.
 5. The device as in claim 2 further comprising: one or morephotonic components or devices formed on the substrate to receive lightfrom or to send light to the optical fiber via the optical waveguide. 6.The device as in claim 1, further comprising: one or more photoniccomponents or devices formed on the substrate to receive light from orto send light to the optical fiber via the optical waveguide.
 7. Thedevice as in claim 1, wherein: the optical fiber located above theoptical waveguide is in direct contact with the optical waveguide and isevanescently coupled to allow light to be coupled between the opticalfiber and the optical waveguide.
 8. The device as in claim 1, wherein:the optical waveguide includes a tapered waveguide terminal thatdecreases in cross section towards a tip of the tapered waveguideterminal; the optical fiber includes a tapered fiber terminal whichdecreases in cross section towards a tip of the tapered fiber terminaland thus tapers in an opposite direction from tapering of the taperedwaveguide terminal; and the tapered fiber terminal and the taperedwaveguide terminal spatially overlap with each other to cause adiabatictransition of guided light and to cause coupling of different modesbetween the tapered fiber terminal and the tapered waveguide terminal.9. The device as in claim 1, wherein the optical fiber has a diametergreater than 200 nm.
 10. The device as in claim 9, wherein the opticalfiber has a diameter less than 20 micrometers.
 11. The device as inclaim 9, wherein the optical fiber has a diameter less than 200micrometers.
 13. The device as in claim 9, wherein the optical fiber hasa diameter less than 300 micrometers.
 14. A photonic device, comprising:a substrate; an input/output multimode optical waveguide formed on thesubstrate and configured to support light in different optical waveguidemodes as an input/output optical port of the substrate, wherein theinput/output multimode optical waveguide includes a tapered waveguideterminal that decreases in cross section towards a tip of the taperedwaveguide terminal; an optical multimode multiplexing/demultiplxingcoupler coupled to the input/output multimode optical waveguide toeither receive different optical signals in different optical singlemodes to combine the received different optical signals into a multimodesignal to the input/output multimode optical wave, or to receive amultimode optical signal from the input/output multimode optical wave tosplit the received multimode optical signal into different opticalsignals in different optical single modes; a plurality of single modeoptical waveguides formed on the substrate and optically coupled to theinput/output multimode optical waveguide to guide, respectively, thedifferent optical signals in different optical modes, either from theinput/output multimode optical waveguide or to the input/outputmultimode optical waveguide; optical processing modules formed on thesubstrate and coupled to the single mode optical waveguides,respectively, wherein each optical processing module is configured toprocess a respective optical signal of a single optical mode; and amultimode optical fiber structured to support light in different opticalfiber modes, the multimode optical fiber located above the input/outputmultimode optical waveguide and optically coupled to the input/outputmultimode optical waveguide via evanescent coupling to allow light to becoupled between the optical fiber and the input/output multimode opticalwaveguide, wherein the multimode optical fiber includes a tapered fiberterminal which decreases in cross section towards a tip of the taperedfiber terminal and thus tapers in an opposite direction from tapering ofthe tapered waveguide terminal, wherein the tapered fiber terminal andthe tapered waveguide terminal spatially overlap with each other tocause adiabatic transition of guided light and to cause coupling ofdifferent modes between the tapered fiber terminal and the taperedwaveguide terminal.
 15. The device as in claim 14, wherein each opticalprocessing module is configured to perform optical filtering in a singleoptical mode.
 16. The device as in claim 14, wherein each opticalprocessing module is configured to perform optical routing from onesingle mode waveguide to another single mode waveguide in a singleoptical mode.
 17. The device as in claim 1, wherein the optical fiberhas a diameter greater than 200 nm and less than 20 micrometers.
 18. Thedevice as in claim 1, wherein the optical fiber has a diameter greaterthan 200 nm and less than 3000 micrometers.
 19. A method for using amultimode optical coupler in coupling light, comprising: spatiallyoverlapping a first multimode optical waveguide having a first spatiallytapered waveguide terminal to adiabatically transition light indifferent first optical modes with a second multimode optical waveguidehaving a second spatially tapered waveguide terminal to adiabaticallytransition light in different first optical modes in an oppositetapering direction of a tapering direction of the first spatiallytapered waveguide terminal, causing optical coupling between the firstoptical modes and the second optical modes; and using the firstmultimode optical waveguide to guide multimode light in the firstoptical modes into the second multimode optical waveguide in the secondoptical modes.
 20. The method as in claim 19, comprising: splitting thelight in the second optical modes from the second multimode opticalwaveguide into individual optical signals in single optical modes;processing the individual optical signals in single optical modes,separately; combining the processed optical signal optical modes into amultimode signal; and directing the multimode signal into a thirdmultimode optical waveguide having a third spatially tapered waveguideterminal to adiabatically transition light in different third opticalmodes with a fourth multimode optical waveguide having a fourthspatially tapered waveguide terminal to adiabatically transition lightin different fourth optical modes in an opposite tapering direction of atapering direction of the third spatially tapered waveguide terminal,causing optical coupling between the third optical modes and the fourthoptical modes to couple the multimode signal into the fourth multimodeoptical waveguide.
 21. The method as in claim 20, wherein the firstmultimode optical waveguide includes a multimode optical fiber.
 22. Themethod as in claim 20, wherein the first multimode optical waveguideincludes a multimode polymer waveguide.
 23. The method as in claim 22,wherein the second and the third multimode optical waveguides areintegrated waveguides formed on a substrate in a photonic chip.